Enigma,
Let me be honest. Your biggest weakness is your GPA. Physics and Engineering grades are less important. What was your Math course GPA ? if it is less than 3.5 (even < 3.7) it is a problem especially for the top programs like Princeton, Stanford, Columbia, NYU and maybe for Berkeley as well. This is the case even if you have very good related work experience.
The 780+ GRE Q score is just one of the essential requirements. The biggest factor is yes, you guessed it right, the quality, rigor of the Mathematics coursework and the applicant's grades in it. Think of it as different layers and Groups
Group A factors (weight 50%)
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1) Number of Math classes (prefer Grad level to differentiate from the crowd)
2) Rigor of the Math coursework. Every engineering undergrad will have good dosage of Math classes like Calculus 1,2,3. But someone with a Mathematics major would have more rigorous curriculum that would include Linear Algebra (more rigorous than applied Linear Algebra taught in engineering),Real Analysis, Complex Analysis, PDE (theoretical), Numerical Analysis (not Numerical Methods), Probability and Stochastic Processes, Mathematical Statistics etc.
Brand name of institution for the Math classes is also very important. Look at the current student profiles at Princeton, Berkeley, NYU and you will get the idea. Stanford and Columbia would be more or less the same.
3) For those with good amount of work experience, time since graduation (reflecting the "rusty" Mathematics knowledge) is a significant factor. Applicants should be able to prove their current ability in Mathematics.
Stanford asks the applicants to include a sheet of Mathematics courses completed with grades and detailed descriptions
Columbia has a separate section as part of the application where applicants have to enter relevant Math Class Name, year taken and the grade obtained
This also helps with Berkeley, NYU applications
Group B factors (weight 30%)
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Personal Essays and Letters of Recommendation
These should reflect the applicants strengths etc...you know the deal here
Group C factors (weight 15%)
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Work experience: Each year, applicants with better and more marketable work experience ( jazzy titles, big IB or HF employers) are appearing. Most of them already have some sort of quant sounding experience. Anyways, if the employer name is good and there is a good letter from one's manager, rest of job functions are not that important and also difficult to verify.
Group D factors (weight 5%)
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Designations like CFA and other Finance Certifications (FRM, PRM usually don't count). Programs in Mathematics and Engineering departments don't give any weight to this category (although a future employer might, especially CFA). B-School programs like Berkeley do give some importance to CFA.
In all, things are becoming very competitive pre and post MFE program. Do a very honest self-assessment.
Even if people here do give your profile a thumbs-up, that doesn't mean anything as your chance of success will depend only on each institutions applicant pool and a little luck
